The short answer is that the BNC to USB adapter you link to will work (though I'm a bit wary of it because it appears to be a generic model) and the Hauppauge card won't because it won't plug into a laptop. And it has the wrong king of connector.

Here's the long answer:

The output of your device is a BNC connector, which is often used in CCTV (closed circuit television) systems such as security cameras.

The video signal from a CCTV camera is in a format called Composite Video. In this format there is no audio and it is at baseband, meaning that it isn't on an RF (radio frequency) carrier that can be transmitted wirelessly.

So you want a digitizer that accepts a composite video signal that is connected via a BNC connector. (Though there are cables that covert between different connector types. For example, from BNC to RCA.)

The next thing to consider is how the digital signal is input into your computer. If your computer is a desktop model then you could buy a video digitizer card that plugs into a PCI card slot. Or PCI Express.

Or you can input the digital signal through a USB port. Of course, this will work with both desktop and laptop computers. Since yours is a laptop, you want the digitizer to output the signal though a USB port.

And that is why your first choice, the BNC to USB digitizer, is the right choice.

You will also have to install software (including a driver) for dealing with the video data. I see that the BNC to USB adapter does include a CD, and that will have the software on it.